{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm\n",
    "import copy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# state A\n",
    "STATE_A = 0\n",
    "\n",
    "# state B\n",
    "STATE_B = 1\n",
    "\n",
    "# use one terminal state\n",
    "STATE_TERMINAL = 2\n",
    "\n",
    "# starts from state A\n",
    "STATE_START = STATE_A\n",
    "\n",
    "# possible actions in A\n",
    "ACTION_A_RIGHT = 0\n",
    "ACTION_A_LEFT = 1\n",
    "\n",
    "# probability for exploration\n",
    "EPSILON = 0.1\n",
    "\n",
    "# step size\n",
    "ALPHA = 0.1\n",
    "\n",
    "# discount for max value\n",
    "GAMMA = 1.0\n",
    "\n",
    "# possible actions in B, maybe 10 actions\n",
    "ACTIONS_B = range(0, 10)\n",
    "\n",
    "# all possible actions\n",
    "STATE_ACTIONS = [[ACTION_A_RIGHT, ACTION_A_LEFT], ACTIONS_B]\n",
    "\n",
    "# state action pair values, if a state is a terminal state, then the value is always 0\n",
    "INITIAL_Q = [np.zeros(2), np.zeros(len(ACTIONS_B)), np.zeros(1)]\n",
    "\n",
    "# set up destination for each state and each action\n",
    "TRANSITION = [[STATE_TERMINAL, STATE_B], [STATE_TERMINAL] * len(ACTIONS_B)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# choose an action based on epsilon greedy algorithm\n",
    "def choose_action(state, q_value):\n",
    "    if np.random.binomial(1, EPSILON) == 1:\n",
    "        return np.random.choice(STATE_ACTIONS[state])\n",
    "    else:\n",
    "        values_ = q_value[state]\n",
    "        return np.random.choice([action_ for action_, value_ in enumerate(values_) if value_ == np.max(values_)])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# take @action in @state, return the reward\n",
    "def take_action(state, action):\n",
    "    if state == STATE_A:\n",
    "        return 0\n",
    "    return np.random.normal(-0.1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# if there are two state action pair value array, use double Q-Learning\n",
    "# otherwise use normal Q-Learning\n",
    "def q_learning(q1, q2=None):\n",
    "    state = STATE_START\n",
    "    # track the # of action left in state A\n",
    "    left_count = 0\n",
    "    while state != STATE_TERMINAL:\n",
    "        if q2 is None:\n",
    "            action = choose_action(state, q1)\n",
    "        else:\n",
    "            # derive a action form Q1 and Q2\n",
    "            action = choose_action(state, [item1 + item2 for item1, item2 in zip(q1, q2)])\n",
    "        if state == STATE_A and action == ACTION_A_LEFT:\n",
    "            left_count += 1\n",
    "        reward = take_action(state, action)\n",
    "        next_state = TRANSITION[state][action]\n",
    "        if q2 is None:\n",
    "            active_q = q1\n",
    "            target = np.max(active_q[next_state])\n",
    "        else:\n",
    "            if np.random.binomial(1, 0.5) == 1:\n",
    "                active_q = q1\n",
    "                target_q = q2\n",
    "            else:\n",
    "                active_q = q2\n",
    "                target_q = q1\n",
    "            best_action = np.random.choice([action_ for action_, value_ in enumerate(active_q[next_state]) if value_ == np.max(active_q[next_state])])\n",
    "            target = target_q[next_state][best_action]\n",
    "\n",
    "        # Q-Learning update\n",
    "        active_q[state][action] += ALPHA * (\n",
    "            reward + GAMMA * target - active_q[state][action])\n",
    "        state = next_state\n",
    "    return left_count\n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Figure 6.7, 1,000 runs may be enough, # of actions in state B will also affect the curves\n",
    "def figure_6_7():\n",
    "    # each independent run has 300 episodes\n",
    "    episodes = 300\n",
    "    runs = 1000\n",
    "    left_counts_q = np.zeros((runs, episodes))\n",
    "    left_counts_double_q = np.zeros((runs, episodes))\n",
    "    for run in tqdm(range(runs)):\n",
    "        q = copy.deepcopy(INITIAL_Q)\n",
    "        q1 = copy.deepcopy(INITIAL_Q)\n",
    "        q2 = copy.deepcopy(INITIAL_Q)\n",
    "        for ep in range(0, episodes):\n",
    "            left_counts_q[run, ep] = q_learning(q)\n",
    "            left_counts_double_q[run, ep] = q_learning(q1, q2)\n",
    "    left_counts_q = left_counts_q.mean(axis=0)\n",
    "    left_counts_double_q = left_counts_double_q.mean(axis=0)\n",
    "\n",
    "    plt.plot(left_counts_q, label='Q-Learning')\n",
    "    plt.plot(left_counts_double_q, label='Double Q-Learning')\n",
    "    plt.plot(np.ones(episodes) * 0.05, label='Optimal')\n",
    "    plt.xlabel('episodes')\n",
    "    plt.ylabel('% left actions from A')\n",
    "    plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:32<00:00, 30.32it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure_6_7()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "rl",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.20"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
